A374787 - OEIS

%I #7 Jul 20 2024 14:41:43

%S 1,4,6,8,10,24,14,32,18,8,22,16,26,56,60,32,34,72,38,80,4,88,46,64,50,

%T 104,108,112,58,48,62,128,132,136,28,16,74,152,52,64,82,16,86,176,180,

%U 184,94,64,98,40,204,208,106,432,20,448,76,232,118,160,122,248

%N Denominator of the mean infinitary abundancy index of the infinitary divisors of n.

%H Amiram Eldar, <a href="/A374787/b374787.txt">Table of n, a(n) for n = 1..10000</a>

%e For n = 4, 4 has 2 infinitary divisors, 1 and 4. Their infinitary abundancy indices are isigma(1)/1 = 1 and isigma(4)/4 = 5/4, and their mean infinitary abundancy index is (1 + 5/4)/2 = 9/8. Therefore a(4) = denominator(9/8) = 8.

%t f[p_, e_] := p^(2^(-1 + Position[Reverse@IntegerDigits[e, 2], _?(# == 1 &)])); a[1] = 1; a[n_] := Denominator[Times @@ (1 + 1/(2*Flatten@ (f @@@ FactorInteger[n])))]; Array[a, 100]

%o (PARI) a(n) = {my(f = factor(n), b); denominator(prod(i = 1, #f~, b = binary(f[i, 2]); prod(k=1, #b, if(b[k], 1 + 1/(2*f[i, 1]^(2^(#b-k))), 1))));}

%Y Cf. A037445, A049417 (isigma), A077609, A374786 (numerators).

%Y Similar sequences: A374777/A374778, A374783/A374784.

%K nonn,easy,frac

%O 1,2

%A _Amiram Eldar_, Jul 20 2024